At the end of this lesson, students will be able to:
Solve an equation using addition.
Solve an equation using subtraction.
Solve an equation using multiplication.
Solve an equation using division.
Terms introduced in this lesson:
Teaching Strategies and Tips
Use the introductory problem to motivate equivalent equations, since it can be solved two ways:
The cost plus the change received is equal to the amount paid, x+22=100.
The cost is equal to the difference between the amount paid and the change, x=100−22
Examples 1 and 2 are essentially the same; constant terms must be added to both sides to isolate x on the left. Adding vertically can benefit students.
Solution. To isolate x, add 4 to both sides of the equation. Add vertically.
The variable in Example 3 is not the usual x. Remind students that the letter of the variable does not matter. Additional Example.
Hint: To isolate n, subtract 14 from both sides of the equation.
In Examples 4-6, teachers may opt to solve the equations by adding the opposite in lieu of subtracting.
Hint: To isolate x, add−8 to both sides of the equation. Add vertically.
Use Example 6 as an example of an equation with fractions. Remind students to find common denominators.
Point out in Example 8 that in general,
which will help students isolate xin one step, multiplying by the reciprocal of a/b.
Note that the equation in Example 10 can be written in dollars or in cents:
5x=3.25 (x in dollars)
5x=325 (x in cents)
Although Examples 13 and 15 can be solved by making a table and Example 14 by guessing and checking, teachers are encouraged to help students setup and solve an equation of the type presented in the lesson.
General Tip: After the constant term is canceled in a one-step equation, the variable must be carried down onto the next line. Remind students to write the x=.
General Tip: Students forget to perform the same operation on both sides of an equation. Have students use a colored pencil to write what they are doing to both sides of the equation.